Aircraft: WIDEBODY; LOW WING; 2 TURBOJET ENG
Phase of flight: Climb
Anomaly: ATC Issue All Types; Airspace Violation All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy

I was notified of an incident that while I was training at R5/6/26. During the training session; neither my instructor nor I were aware of the event; however; after watching the event on FALCON; we were made aware of the event and recalled details that may have led to the occurrence of the event. Aircraft X departed MIA (landing Central America). W174C and W465 A/B were active. Aircraft X was cleared 'direct VRGAS direct TADPO rest of route unchanged' to miss W465A and issued a climb instruction to climb to FL370. As the aircraft progressed towards TADPO there was no opposite direction traffic for the aircraft; however; volume and complexity increased due to the combination of sectors and priorities happening in other areas of the sector. When Aircraft X was in the vicinity of MTH or just south of MTH; the Controller at Havana Center called and spoke to my D-side. As the aircraft; got closer to TADPO; I believe I asked my D-side if the radar handoff on Aircraft X had been made; but I can't be sure. I do not remember if the flight progress strip had been updated with a circled 'R;' or if an 'R' had been entered into the 4th line of the flight data block. I transferred communications of Aircraft X to Havana Center while the aircraft was still in a climb to FL370. At the same time; Havana Center had Aircraft Y northbound toward TADPO at FL380. In accordance with the Havana Center/Miami Center LOA; the Havana Center Controller descended Aircraft Y to FL360 prior to TADPO as Aircraft X crossed the center boundary. While; the two aircraft were not in immediate proximity according to Miami Center (7110.65) standards; Havana Center (in an e-mail sent to Quality Assurance); said that drastic action was taken to turn Aircraft X; though a proximity event didn't occur. The message from Havana Center indicated that they had no flight plan information on the aircraft and that a handoff had not been made. My FLM informed me after watching FALCON that a handoff had not been made (according to the D-side and R-side recordings). During the time that Aircraft X was progressing toward TADPO; several other things were happening that impeded my ability to verify the radar handoff. Several MIA departures came onto the frequency after Aircraft X; a military aircraft that had been operational; wanted an IFR clearance; and VFR traffic was picking up in the Marathon Low sector. In addition; I was in the process of trying to split the Marathon Low (R5) sector off amidst the calls from traffic. I recommend that since this occurred on a day of the ERAM test run; that someone look into why Havana Center received no flight plan information on Aircraft X. They received information on at least two subsequent MIA departures that were on my scope at the same time; but failed to identify Aircraft X; which was closer to their boundary. Flight plan processing to and from Havana Center will need to be seamless in order to not have this occur again once ERAM is fully operational 24/7. Aircraft X entered Havana Center airspace without the required manual hand off being performed. I was informed of this event eleven days after it occurred. I have no recollection of the exact circumstances as they happened.None of the sector team remembers where the breakdown occurred; whether the D-side who would usually perform the hand off misunderstood the Havana Controller and thought the aircraft was in radar contact; or if there was a miscommunication between the D-side and the R-side trainee/trainer about whether the aircraft was handed off. The R-side thought the aircraft had been handed off; and transferred communications to Havana Center.Communication with Aircraft X was transferred approximately one to two minutes before the aircraft entered Havana Center airspace. Havana Controller did not inquire about the incident at that time or subsequently.First and foremost; I must ensure that aircraft are properly handed off to adjacent facilities before radio communications are transferred.The safe and efficient flow of aircraft is dependent upon everyone working together toward that goal. This includes adjacent facilities working together. As human errors occur; we must work together to address and correct them as quickly as possible. If Jacksonville or Houston Center were to erroneously ship an aircraft to me without my having accepted the radar handoff; I would immediately reach out to them via land line to acquire radar contact. I believe that they would do the same for me. Once an error like this has occurred; the focus should be upon transferring radar identification for the sake of safety.Radio communications were transferred; and therefore Havana Center was presumably talking to; Aircraft X for as much as two full minutes before the aircraft entered their airspace. At any point during that time; they could have called us to affect a handoff. If they had no idea who the aircraft was; they should have told him to return to last assigned frequency. Either of these actions would have been much safer than simply allowing the aircraft to enter their space. Again; it is my job to ensure timely hand offs before the transfer of communication. I also feel that once an error has been identified by a sector; the immediate focus should be upon working with adjacent facilities to correct it and ensure the safe and expeditious flow of aircraft. Two reporters are made aware of an aircraft that was not handed off after returning to work at a later date. Operational error occurred due to this issue.